Do not shake your keg prior to burping.
Burping means gassing the keg up with Co2 and then releasing the pressure through the release valve. This is done three or four times, then the keg is repressurized and left somewhere quietly at correct fermentation temperatures so that carbonation occurs (assuming you are naturally carbonating.) Then the keg is moved to a cooler location if you have one. The fridge would be ideal if you have enough fridge space.
Burping flushes most of the oxygen from the headspace, allows you to check for leaks and seals the keg. Oxygen is the enemy of finished beer. Limiting the contact of your finished product with oxygen will extend its long term stability. If you drink the beer almost immediately, this may not be an issue. If you leave the keg for six months before consuming, it is definitely a big issue.
Oxidisation shows up as wet carboard aromas and sherry aromas and is part of the gradual decay in the flavours of your beer.
This is why when racking beers, people take great care to transfer to a container with minimal headspace, it is done carefully with minimal splashing and a racking tube is used. When bottling, a bottling tube is used for the same reason. People who fill bottles from their keg tap also take great care and will often use a counter pressure bottle filler which allows the bottle to be flushed with CO2 before filling.
Do not shake your keg prior to burping. There should be no need to shake your keg if you have used a priming solution and racked onto it. The priming solution will quickly be mixed into the beer as it is racked into the keg. Shaking your keg prior to burping is one place where oxygen will be introduced into the beer